Penalized regression calibration: a method for the prediction of survival outcomes using complex longitudinal and high-dimensional data

TL;DR

This paper introduces penalized regression calibration (PRC), a novel method for predicting survival outcomes using complex longitudinal and high-dimensional data, incorporating mixed effects modeling and a bootstrap validation correction.

Contribution

The paper presents PRC, a new approach combining mixed effects models and penalized Cox regression for survival prediction with longitudinal high-dimensional data, including a validation correction method.

Findings

PRC performs well in simulation studies.

PRC effectively predicts time to loss of ambulation in Duchenne muscular dystrophy.

The R package pencal facilitates implementation of PRC.

Abstract

Longitudinal and high-dimensional measurements have become increasingly common in biomedical research. However, methods to predict survival outcomes using covariates that are both longitudinal and high-dimensional are currently missing. In this article, we propose penalized regression calibration (PRC), a method that can be employed to predict survival in such situations. PRC comprises three modeling steps: First, the trajectories described by the longitudinal predictors are flexibly modeled through the specification of multivariate mixed effects models. Second, subject-specific summaries of the longitudinal trajectories are derived from the fitted mixed models. Third, the time to event outcome is predicted using the subject-specific summaries as covariates in a penalized Cox model. To ensure a proper internal validation of the fitted PRC models, we furthermore develop a cluster bootstrap optimism correction procedure that allows to correct for the optimistic bias of apparent measures of predictiveness. PRC and the CBOCP are implemented in the R package pencal, available from CRAN. After studying the behavior of PRC via simulations, we conclude by illustrating an application of PRC to data from an observational study that involved patients affected by Duchenne muscular dystrophy, where the goal is predict time to loss of ambulation using longitudinal blood biomarkers.